Is Classical Mechanics in Fact Deterministic?

Abstract

The laws of classical mechanics, and through them the laws of classical physics as a whole, are so constructed that, if the variables in a closed system are given at some initial point of time, they can be calculated for any other instant—in principle, at least; for it is in most cases beyond human ability to carry out the mathematics involved. This deterministic idea has greatly attracted many thinkers, and has become an essential part of scientific philosophy. Modern physics, however, has been compelled to abandon determinism, together with other time-honored theories of space, time and matter, under the pressure of new empirical discoveries. Quantum mechanics, which has taken over the place of Newtonian mechanics, allows only statistical statements concerning the behaviour of mass particles. The great majority of physicists have become reconciled to this state of affairs, for it corresponds exactly to the empirical situation in atomic and nuclear physics, where experiments are based fundamentally on the counting of events. Among the theoreticians, however, there are some who are not content, and they are indeed some of the great ones to whom the quantum theory owes its origin and development. So far as I know, Planck himself was always sceptical towards the statistical interpretation of quantum mechanics. The same is true of Einstein; even today he continues to point out, by means of ingenious examples, contradictions in this interpretation (and he is, moreover, still more concerned with the resolution of the concept of physical reality, which is closely involved with the problem of determinism). Schrödinger goes still further; he proposes to abandon the concept of particles (electrons, nuclei, atoms, etc.) and to construct the whole of physics upon the idea of waves, which obey deterministic laws in accordance with wave mechanics. De Broglie (and others) take the opposite course; they reject waves, and seek a reinterpretation of quantum mechanics, in which everything is in principle determinate, and an uncertainty in prediction arises only by the presence of concealed and unobservable parameters. None of these physicists denies that quantum mechanics within the realm of its validity, i.e., apart from the theory of elementary particles, is in agreement with experiment and meets all the demands of the experimenters. Their rejection is in every case founded on the assertion that the usual interpretation of the quantum formulae is obscure and philosophically unsatisfactory.